I was wondering about Thranduil's words at the end of the Hobbit that Legolas should seek out one called 'Strider,' Firstly is this the same person as the Aragorn in Lotr? Or could other Dunedian leaders have that nickname? Possibly as everything in PJ's Middle-Earth is more truncated than Tolkien's it possibly is. But even then Legolas has a long way to go and a bit of searching to do. To the Misty Mountains, over the Misty Mountains then to the wild of Eraidor. I don't think that there is any evidence that Legolas did this, but one never knows!

My best guess is that Aragorn in the films met Éowyn in March of 3002, just after his eighty-seventh birthday (in Tolkien's legendarium the Three Hunters arrived at Edoras with Gandalf the White just after Aragorn's eighty-eighth birthday in the year 3019). That would make him twenty-five years old at the time of the Battle of Five Armies in Peter Jackson's The Hobbit: The Battle of the Five Armies (year 2940, sixty years before Bilbo's birthday party of September 22, 3000). So he would indeed have been a young Ranger as Thranduil describes. If Thranduil had met Aragorn then it seems more likely that the Ranger came to the Woodland Realm, though the Elvenking might have met him during a hunt or an outdoor feast rather than at court.

Legolas in film-canon could have followed his father's advice and gone off to find this Strider. He might not even have had to journey to Eriador; though it doesn't seem likely to me that he was east of the Misty Mountains during the Quest of Erebor. "For a brief time I was here; and for a brief time I mattered." - Harlan Ellison

I got the impression that Legolas and Aragorn already knew each other.

That impression was created by Legolas' animated defense of Aragorn against Boromir's scorn at the Council of Elrond and a general air of familiarity between the two characters through the trilogy. I watched the movie again recently and still felt that way.

So Thranduil's suggestion in BOTFA that Legolas seek out Strider made sense to me, even while I thought it was a trifle silly.

...within Tolkien's legendarium Aragorn and Legolas knew each other at least from the time of the Ranger's capture of Gollum and possibly from much earlier. It is entirely possible that, in both films and books, they first met during the early years of Aragorn's wanderings. "For a brief time I was here; and for a brief time I mattered." - Harlan Ellison

Definitely in the movies, maybe not in the books – but even there, as Otaku-sempai pointed out, they would have had chances to meet each other, so I think a meeting before the War of the Ring would not be out of the question.